Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/43409
Title: Persistency and Stein's Identity: Applications in Stochastic Discrete Optimization Problems
Authors: ZHENG ZHICHAO
Keywords: Persistency, Stein's Identity, Distribution Approximation, Quadratic Regret, Project Management, Portfolio Selection
Issue Date: 10-May-2013
Source: ZHENG ZHICHAO (2013-05-10). Persistency and Stein's Identity: Applications in Stochastic Discrete Optimization Problems. ScholarBank@NUS Repository.
Abstract: This thesis explores the connection between stochastic discrete optimization problem and classical probability theory, Stein?s Identity, to solve two classes of problems. The first problem is to approximate the distribution of the optimal value of a mixed zero-one linear optimization problem under objective uncertainty. We develop a least squares approximation framework and demonstrate its application in the project management problem. The second problem is decision making under uncertainty, for which we propose a new decision criterion, quadratic regret. Using the portfolio management problem, we illustrate the features of this new criterion, in particular, its close relationship with a common behavioural abnormality, probability matching. By resorting to Stein?s Identity, we transform both problems into corresponding persistency estimation problems under the normal uncertainty assumption. We derive the closed-form solutions for both models and discuss the advantages of this new approach over existing solution methods both analytically and numerically.
URI: http://scholarbank.nus.edu.sg/handle/10635/43409
Appears in Collections:Ph.D Theses (Open)

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